MATH 613 Modular forms (Topics in Number Theory).

MATH 613 Modular forms (Topics in Number Theory)

Text:

The course will be largely based on James Milne's notes and F. Diamond and J. Shurman "Introduction to modular forms" (available online at UBC library). We will also somtimes use the classic textbook T. Miyake, "Modular forms" (available online at UBC library). We will occasionally refer to several other sources, including:

William Stein, "Modular Forms, a computational approach"
S. Lang, "Introduction to modular forms" and "Elliptic Functions".

Classes: Tue, Th 2-3:30pm in CEME (Civil and Mechanical Engineering), Floor 1, room 1210.
My office: Math 217.
e-mail: gor at math dot ubc dot ca
Office Hours: for now, by appointment.

Course outline

Announcements

HOMEWORK

There will be approximately bi-weekly homework assignments.

Here are some resources if you you need resources for using TeX.

Detailed Course outline

Short descriptions of each lecture and relevant additional references will be posted here as we progress.

Tuesday January 6 : Lecture 1. Overview and motivation; the definition of modular forms; Riemann surfaces (approximately matching Milne's Introduction).

Thursday Sep. 8 : Lecture 2. The goal (to be achieved next class) is to define the structure of a Riemann surface on "H mod Gamma". We did: 1. A quick survey of actions of topological groups (see Milne, Section 1 (pp. 13-14) and Part 1 of the homework 1) with the end result that "H mod Gamma" has Hausdorff quotient topology;
2. Classification of Fractional-linear transformations, with an aside on realizing the Riemann sphere as the projective line over C (see homework). (Milne, pp.30-31, not including Remark 2.11 which will be discussed later).